Some estimates for multilinear Calderón-Zygmund operators with fractional kernels of Dini’s type and their commutators on generalized fractional mixed Morrey spaces

Key Points

• The aim is to explore the boundedness of multilinear Calderón-Zygmund operators with fractional kernels and their commutators in specific function spaces.
• Studied boundedness using the extrapolation theorem and monotone convergence theorem.
• Analyzed fractional integral operator on mixed Lebesgue spaces.
• Derived results on generalized fractional mixed Morrey spaces based on earlier findings.
• Proved boundedness of commutators connecting different spaces.
• Showed multilinear Calderón-Zygmund operators are bounded in L^{ ext{q}} spaces.
• Established boundedness in generalized fractional mixed Morrey spaces L^{ ext{q}, ext{η}, ext{ψ}}.
• Proved boundedness of commutators T_{b,1} and T_{b,2} in the same space.
• Demonstrated applications for the multilinear fractional new maximal operator and related commutators.

Abstract